COMPARATIVE ANALYSIS OF SOME PROMINENT MCDM METHODS : A CASE OF RANKING SERBIAN BANKS

In the literature, many multiple criteria decision making methods have been proposed. There are also a number of papers, which are devoted to comparison of their characteristics and performances. However, a definitive answer to questions: which method is most suitable and which method is most effective is still actual. Therefore, in this paper, the use of some prominent multiple criteria decision making methods is considered on the example of ranking Serbian banks. The objective of this paper is not to determine which method is most appropriate for ranking banks. The objective of this paper is to emphasize that the use of various multiple criteria decision making methods sometimes can produce different ranking orders of alternatives, highlighted some reasons which lead to different results, and indicate that different results obtained by different MCDM methods are not just a random event, but rather reality.


INTRODUCTION
The multiple criteria decision making (MCDM) can be generally described as the process of selecting one from a set of available alternatives, or ranking alternatives, based on a set of criteria, which usually have a different significance.
In the past, these methods have been used to solve many problems, which are documented in many professional and scientific journals.Numerous prominent papers presented research in MCDM, which is why we omit the reference to them in this paper.
The above-mentioned MCDM methods transform multiple criteria decision-making process, i.e., Multiple Criteria optimization, in a single criterion decision-making optimization, which is much easier to solve.A number of authors have been identifying different phases (stages) in MCDM process, from which, in order to more clearly point out the objectives of this study, the following phases are emphasized: -criteria weights determination, -normalization, -aggregation, and -selection.
A typical MCDM problem can be precisely presented in the following form: (1) where D is decision matrix, x ij is performance of i-th alternative with respect to j-th criterion, W is weight vector, w j is weight of j-th criterion, i = 1,2, … m; m is the number of compared alternatives, j = 1,2, ..., n; n is the number of the criteria.
Information stored in a decision matrix is usually incommensurable, i.e. performance ratings in relation to different criteria are usually expressed using different units of measure.Therefore, data should be transformed into comparable values, using a normalization procedure.For normalization, numerous procedures, also known as normalization methods, have been formed.A comprehensive overview of some normalization procedures were given by Zavadskas and Turskis (2008).
Evaluation criteria involved in the MCDM models can be classified in several ways.In this paper two, very significant classification, of evaluation criteria are considered.
In relation to required direction of optimization, there are two types of evaluation criteria, namely: -benefit type criteria, i.e., the higher rating is better; and, -cost type criteria, i.e., the lower rating is better.
Evaluation criteria can also be classified as subjective and objective.Subjective criteria have a qualitative nature, i.e., performance ratings of these criteria are rather expressed using quantitative values, often using linguistic variables.In contrast, objective criteria have a quantitative nature, i.e., the performance ratings of these criteria are rather expressed using quantitative values, which is why performance ratings of these criteria can be much more precisely determined.
In MCDM, evaluation criteria usually have different importance (weights), and it is also important that weights of criteria often have a large impact on selection of the most acceptable alternative.
N-dimensional information, stored in a MCDM model, can be transformed into onedimensional using MCDM methods.As is mentioned above, over time, many MCDM methods were proposed.They differ in the approach used to determine the most appropriate alternative, that is, they have different aggregation procedures, use different normalization methods and have different treatment for the cost and benefit criteria.
Therefore, 'Which is the best method for a given problem?' has become one of the most important and challenging questions (Triantaphyllou, 2000).However, the question 'Whether all MCDM methods give the same results?' is also important and actual too.
In this paper, one case study of ranking Serbian banks was considered, using some of the most prominent MCDM methods.This paper examines comparison of results that were achieved using these methods.
Therefore, this paper is organized as follows: In section 2 of this paper, one brief review of some of the most prominent MCDM method is given.In section 3, a case study of ranking Serbian banks, based on objective criteria, is considered.After that, in section 3, several variants of discussed case study are discussed with the aim to determine whether different normalization methods, different aggregation procedures and different criteria weight have impact on the selection of the most acceptable alternative, or a ranking order of the considered alternatives.Finally, section 4 presents conclusions.

A BRIEF COMPARATIVE OVERVIEW OF SOME OF THE MOST PROMINENT MCDM METHODS
In this section, a brief comparative overview of some prominent MCDM methods is presented.In order to perform their clearer and more precise comparison, some labels in formulas or parts of formulas are adjusted with accepted style.
From many methods which can be used for selecting and/or ranking different alternatives, in this paper, we consider following: SAW, ARAS, COPRAS, MOORA, GRA, CP, VIKOR and TOPSIS method.
One of main objectives that had been planned as a result of this study was the formation of a simple to use MCDM model for ranking commercial banks.Therefore, in this study the MCDM methods that require significant user interaction during problem solving was process omitted, such as ELECTRE and PROMETHEE methods.This is the reason why the AHP method was also omitted.However, the pairwise comparison approach, taken from the AHP method was used to determine the weights of criteria.

Simple Additive Weighting (SAW)
Simple additive weighting (SAW) method is probably the simplest, best known and formerly often used MCDM method.The SAW method uses a simple aggregation procedure, which can be presented using the following formula: where Q i is overall ranking index of i-th alternative; w j is weight of j-th criterion, r ij is normalized performance of i-th alternative with respect to j-th criterion, i = 1,2, … m; and j = 1,2, ..., n.
In SAW method, the alternatives are ranked on the basis of their Q i in ascending order, and the alternative with the highest value of Q i is the best ranked.The best ranked, or the most preferable, alternative, based on the SAW method, A * SAW can be determined using the following formula: . (3) The aggregation procedure in SAW method makes no difference between cost and benefit type criteria.Therefore, cost type criteria must be transformed into benefit type criteria during normalization.
Formerly, this form of transformation was often stated as a weakness of SAW method.However, in some actual fuzzy extensions of prominent MCDM methods, cost type criteria also are transformed into benefit type criteria, such as in Saremi et al. (2009), Mahdavi et al. (2008), Wang and Elhag (2006).
SAW method can be used with different normalization procedures.Linear scale transformation -Max method is probably the most frequently used normalization procedure, but there are also other approaches.
Some typical normalization procedures, used in the SAW method, are given below: where is the largest performance ratings and is the smallest performance rating of j-th criterion, Ω max and Ω min are sets of benefit and cost criteria, respectively.
As already stated, SAW method was previously frequently used.However, the usage of some recent MCDM methods significantly reduced the use of SAW method, but this simple and effective MCDM method is not forgotten.Moreover, it continues to be developed and used, as proven by its fuzzy and grey extensions, such as: Chen ( 2012

(ARAS) A new Additive Ratio ASessment
A new additive ratio assessment (ARAS) method is newly proposed MCDM method.In this method, the most acceptable alternative is determined on the basis of degree of utility Q i , which can be calculated using the following formula: where S i is overall performance index of i-th alternative, S 0 is overall performance index of optimal alternative, and S 0 usually has a value which is 1.
The alternatives are ranked on the basis of their Q i in ascending order, and the alternative with the highest value of Q i is the best ranked.The best ranked alternative, based on the ARAS method, A* ARS can be determined using the following formula: . ( 9) The specificity of ARAS method, compared to other methods, is the introduction of the optimal alternative A 0 .The performances of the optimal alternative are determined on the basis of decision makers' preferences.If the decision maker has no preference about some criterion, its optimal performance is determined as follows: . (10) The ARAS method uses the same aggregation procedure as the SAW method, and therefore the overall performance index of any alternative can be determined as follows: . (11) The normalized performance ratings in ARAS are calculated by using the following formula: . ( The ARAS method can be classified as an effective and easy to use MCDM method.Although it is newly proposed, it has been applied to solve various decision-making problems, and its fuzzy and grey extension have also been proposed, named ARAS-F (Turskis & Zavadskas, 2010b) and ARAS-G (Turskis & Zavadskas, 2010a).From many papers where the use of ARAS method and its extensions is discussed, just few are mentioned here: Zavadskas et al. (2012), Turskis et al. (2012), Kersuliene and Turskis (2011), Susinska et al. (2011), Bakshi and Sarkar (2011).

(COPRAS) COmplex PRoportional ASsessment
Complex proportional assessment (COPRAS) method, compared to previous methods, has slightly more complex aggregation procedure, but it does not require transformation of cost to benefit type criteria.The overall ranking index, of each alternative, can be calculated using the following formula: , where . ( 16) The Formula ( 13) can be also written in following simplified form: The alternatives, by COPRAS method, are ranked on the basis of their Q i , and the alternative with the highest value of Q i is the best ranked.The best ranked alternative, based on the COPRAS method, A* CPS can be determined using the following formula: . ( 18) For normalization, COPRAS method uses linear transformation -Sum method, without transformation of cost to benefit type criteria.The normalized performance ratings in COPRAS are calculated using the following formula: Description of COPRAS methods and possibilities of its application are published in a large number of papers, such as: As for other MCDM methods, fuzzy and grey extension is also proposed for COPRAS method.Fuzzy extension of COPRAS method, COPRAS-F method was introduced by Zavadskas and Antucheviciene (2007), and it used to analyze abandoned building's regeneration alternatives in Lithuanian rural areas.Zavadskas et al. (2008a) proposed a grey extension of COPRAS methods, called GOPRAS-G method, and used it to select dwelling house walls, project managers (Zavadskas et al. 2008b), contractors (Zavadskas et al. 2008c), and so on.
Since then, the COPRAS method and its extensions has been applied for solving decision-making problems.As some significant examples of applying COPRAS and COPRAS-G method can be mentioned:

(MOORA) The Multi-Objective Optimization by Ratio Analysis
The multi-objective optimization by ratio analysis (MOORA) method consists of two parts, which are named: Ratio system approach and Reference point approach.These two parts are based on the same type of normalization.
Ratio system approach.The basic idea of the Ratio system approach of the MOORA method is to determine the overall performance index of alternative as the difference between sums of weighted normalized performance of benefit and cost criteria, as follows: . (20) The alternatives are ranked on the basis of their S i in ascending order, and the alternative with the highest value of S i is the best ranked.The best ranked alternative, based on the Reference point approach of the MOORA method, A* MRS can be determined using the following formula: . ( 21) Reference point approach.After considering the most important reference point metrics, Brauers and Zavadskas (2006) emphasize that the min-max metric is the best choice amongst them.Therefore, for optimization based on the reference point approach Brauers and Zavadskas (2006) proposed the following formula: . ( 22) The best ranked alternative, based on Reference point approach of the MOORA method, A* MRP can be determined using the following formula: For normalization, MOORA method uses vector normalization procedure, without transformation of cost to benefit type criteria.The normalized performance ratings in MOORA method are calculated using the following formula: . ( The MOORA method is also a newly proposed MCDM method.Although the MOORA is a newly proposed method, it is applied to solve many economic, managerial and construction problems, and is presented in a significant number of papers published in journals, such as: Brauers andZavadskas (2006, 2009) Brauers and Zavadskas (2010a) also presented MULTIMOORA method, as an extension of MOORA method with full multiplicative form.As MOORA method, MULTIMOORA method is also widely used for solving numerous problems.From many papers few are mentioned here: Brauers and Zavadskas (2010a, 2010b, 2011) Actuality of MOORA method also confirms a significant number of papers which have been published in numerous journals.In addition to the previously mentioned papers, below are given some new and significant, such as: Brauers and Zavadskas (2012), Chakraborty and Karande (2012), Archana and Sujatha (2012).where L p,i is distance metric of i-th alternative for a given parameter p, and are the most preferable and the worst performance rating of j-th criterion, and p is metric, .The parameter p, in formula ( 25) is used to represent the importance of the maximal deviation from the reference point.By varying the parameter p from 1 to infinity, it is possible to move from minimizing sums of individual deviations to minimizing the maximal deviation to the ideal point.

(CP) Compromise Programming
The most preferable and the worst performance rating of j-th criterion are determined using the following formulae: , . ( 27) The alternatives are ranked on the basis of their L p,i in descending order, and the alternative with the lowest value of L p,i is the best ranked.The best ranked alternative, based on the CP method, A* CP can be determined using the following formula: . (28) Unlike the previously described MCDM methods, the aggregation procedure used in CP method also performs normalization of ratings, and because of that the normalization procedure does not have to be performed.
In the past, the Compromise programming methodology has made a prominent use in the field of water resources management, but it is also applied in many other fields, such as forest management and economy.Some of the more important studies that are based on the use of Compromise programming can be specified in the following: Wu and Chang ( 2004

(GRA) Grey Relational Analysis
Grey relational analysis (GRA) was proposed as part of Grey system theory.Similar to the TOPSIS method, GRA is based on the use of the distance from an ideal solution.In the literature, many authors have discussed the use of different variants of the GRA, from which we, in this paper, present one simple and efficient which can be used when ratings are expressed with the crisp numbers.
In GRA, the most appropriate alternative is determined on the basis of Grey relational grade, which can be calculated using the following formula: where is the grey relational coefficient of i-th alternative to the j-th criterion.
The grey relational coefficient of each alternative can be calculated using the following formula: , (30) where is most preferable normalized performance rating of i-th alternative according to j-th criterion, is the distinguish coefficient, and .The coordinates of the ideal point, i.e., the most preferable normalized ratings in relation to the criteria, can be determined using the following formula:

, (31)
where A* is ideal point, also known as ideal solution, is j-th coordinate of ideal point, is normalized performance rating of i-th alternative to the j-th criterion, and Ω max and Ω min are sets of benefit and cost criteria, respectively.
Different authors use GRA with various normalization procedures, with or without transformation of cost type to benefit type criteria.In this paper, the use of GRA without transformation of cost type to benefit type criteria was discussed.Therefore, the normalized performance ratings can be calculated by using one of the following formulae: or the formulae ( 19) and ( 24).After determining overall ranking index for each alternative, in GRA approach the alternative with smallest overall ranking index has higher priority (rank) and the most acceptable alternative can be determined by the following formula: . (34) Beside the above presented GRA approach, in the literature also are proposed some complex variant of GRA which are based on the well-known concept used in TOPSIS method, i.e., TOPSIS based GRA approach.Due to a clearer presentation, in this paper TOPSIS based GRA approach is marked as GRA(T) approach.
In the GRA(T) approach, the best ranked alternative can be determined using the following formula: where: , (37) and, , . ( 39) As it can be concluded from the above, selection of the best placed alternative using TOPSIS based GRA approach is based on the ratio between distance of an alternative from the ideal and non-ideal solution.
Therefore, in TOPSIS based GRA approach, there are two characteristic points in n-dimensional space, i.e. ideal and antiideal point, also known as ideal and antiideal solution.
The ideal point is determined as already shown in formula (31).The anti-ideal point is determined as follows: , (40) where Ais anti-ideal point, is j-th coordinate of anti-ideal point.
GRA approach is used to solve many decision-making problems.The achieved results, and the usability of the GRA approach, are presented in a number of papers published in many significant journals.From many papers, some most prominent are mentioned here: Chan and Tong (2007), Tosun (2006), Fung (2003), Lin et al. (2002), Fu et al. (2001).

VIKOR method
The development of the VIKOR method, similar to CP method, also started from the Minkowski L p metric, already shown by formula (25).The VIKOR method uses two characteristic metrics to formulate ranking measure, p = 1 and p → ∞, for which the formula (25) gets the following specific forms: (41) (42) where S j and R j as the average and the worst group score of i-th alternative.
The VIKOR method is based on idea of ideal and compromise solution, and the overall ranking index for each alternative is calculated using the following formula: (43) where: , ( 44) , ( 45) , ( 46) and ν is significance of the strategy of criteria (objectives) majority which value is usually set to be 0.5.Compared to other previously considered MCDM methods, determination of the most appropriate alternative using VIKOR method is more complex, and it can be described as follows: The alternatives are sorted by values S, R and Q in the ascending order.The most acceptable alternative A' is the one with the minimum value of Q, if two complementary conditions are satisfied (Opricovic & Tzeng 2004):

C1. Acceptable advantage:
The condition C1 is satisfied if the following equation is satisfied: where: (49) A" is the alternative having the second position in the ranking list by Q, and m is the number of alternatives.

C2. Acceptable stability in decision making:
Alternative A' must also be the best ranked by S and/or R.
If one of these conditions is not satisfied, then, a set of compromise solutions with the advantage rate is proposed instead of most acceptable alternative (Antucheviciene et al. 2011).This set will consist of: -the alternatives A' and A"; if only condition C2 is not satisfied, or -the alternatives A',A",..., A n ; if conditions C1 and C2 are not satisfied, where A n is determined by the relation: . (50) The VIKOR method has been used for solving numerous MCDM problems.In order to solve complex decision-making problems Opricovic ( 2007) proposed a fuzzy extension of VIKOR method, named VIKOR-F.Sayadi et al. (2009) also proposed a grey extension of VIKOR method.
The important characteristic of this method is that the number of papers published in the last two years has increased significantly compared to the previous period.From many papers few are mentioned here: Opricovic, S. ( 2011

TOPSIS method
The TOPSIS method is one of the most widely used MCDM methods.The basic principle of TOPSIS method is that the best alternative should have the shortest distance from the ideal solution and the farthest distance from the anti-ideal solution.A relative distance of each alternative from ideal and anti-ideal solution is obtained as: where and are separation measures of alternative i from the ideal and anti-ideal solution, respectively; C i is relative distance of alternative i to the ideal solution, and .
. The largest value of the criterion C i correlates with the best alternative.Therefore, in TOPSIS method, the alternatives are ranked on the basis of their C i in ascending order, and the alternative with the highest value of C i is the best ranked.The best ranked, or the most preferable, alternative can be determined using the following formula: . (52) The separation measures of each alternative, from the ideal and anti-ideal solution, are computed using following formulae: , and . (54) The ideal A* and the anti-ideal Asolution in TOPSIS method can be determined using the already mentioned formulae ( 31) and ( 40), respectively.It can be seen from the formulae ( 53) and ( 54) that ordinary TOPSIS method is based on the Euclidean distance.In addition to Euclidean distance, in the literature are also presented some examples where TOPSIS method was used with other metrics, especially with a city-block distance (Chang et al., 2010;Shanian & Savadogo, 2006;Yoon & Hwang, 1980).
TOPSIS method, as well as the MOORA method, uses Vector normalization procedure, already given by formula (24).However, in the literature is also discussed the use of TOPSIS method with other normalization procedures, especially when its fuzzy extensions are proposed, such as in Saremi et al. ( 2009), Yang and Hung ( 2007), Wang and Elhag (2006), and so on.
TOPSIS is one of the most actual MCDM methods, which is confirmed by a number of papers published in scientific journals in 2012.From a very large number, just a few are mentioned here, such as: Tansel (2012), Ravi (2012), Huang and Peng (2012), Buyukuzkan (2012), Arslan and Cunkas (2012).
In the past, TOPSIS method was used rather frequently.This is also confirmed by a number of papers, such as: Boran et al.

A CASE STUDY AND DISCUSSION OF RESULTS
In this section we consider a case study of ranking some Serbian commercial banks.In order to perform more objective conclusions in terms of the applicability of MCDM methods, the influence which the weights of criteria, the used approaches and the applied normalization procedure have on the selection of the most appropriate alternative and obtained ranking orders of alternatives, is also taken into consideration in this section.

A Case Study: The Case of ranking Serbian banks
In the literature, many papers have been devoted to the ranking of banks, as well as to determining banks' performances.Among many, here are mentioned only a few, such as: Ferreira et al. ( 2012 2009), Rakocevic and Dragasevic (2009), Ginevicius and Podvezko (2008), Hunjak and Jakocevic (2001), Yeh (1996), Sherman and Gold (1985).
This case study presents the ranking results of five commercial banks in Serbia, based on objective criteria.These criteria and their sub-criteria, adopted from Yeh (1996) and Hunjak and Jakocevic (2001), are shown in Table 1.
Weights of criteria, sub-criteria and the resulting weights, obtained on the basis of pairwise comparisons, are shown in Table 2. Due to limited space, the calculation procedure is omitted.
Ratings, i.e. performance ratings, of the considered banks, in relation to selected evaluation criteria, are shown in Table 3.These ratings are calculated based on data available on the web sites of the considered banks, i.e. financial reports for 2011 year, and data available on the website of the National Bank of Serbia.

Table 1. Quantitative criteria for bank performance determination
The ranking of banks was started using SAW method.The results of ranking banks obtained using SAW method and various normalization procedures are shown in Table 4.
Based on data from Table 4, it can be determined that SAW method, used with various normalization procedures, gave different alternatives as the best ranked.It might be a little confusing.
The obtained rankings orders, shown in the column VII of Table 4, also look confusing.By applying the same MCDM method and various normalization procedures, different ranking orders are obtained.
In order to resolve doubts about the best ranked alternative, ranking of banks was again performed using various MCDM methods.Obtained ranking results are shown in Table 5.
Due to easier comparison, in Table 5 are repeated results obtained by the SAW method used with Max and MaxMin normalization procedures.
From Tables 4 and 5 can be seen that there is a certain similarity in results obtained by using so-called performance-based methods, such as ARAS, COPRAS, MOORA(RS) and SAW method used with Max normalization procedure.

Table 2. Relative weights of evaluation criteria Table 3. Initial decision matrix -banks' performances and criteria weights
Note: Table 3 does not contain information on all banks which operate in Serbia.This table contains only performance ratings for some characteristic bank.
A deviation from the identified similarities in achieved results can be seen in the case of using GRA approach.In addition, in case of using CP, and p = 1, the deviation is more noticeable, and obtained results are the same as when the SAW method with MaxMin normalization procedure is used.
As is stated in subsections 2.5 and 2.6, the   GRA and CP methods are based on the idea that the best placed alternative has the smallest distance from the ideal point (solution) and therefore they can be placed in so-called distance-based approach methods.If more detailed consider the MaxMin normalization procedure, which is shown by formula (7), we can notice that its use transforms SAW method into so-called distance-based approach methods, instead of the usual performance-based approach which is obtained using Max, Sum or Vector normalization procedures.Therefore, a weak correlation observed in the results obtained by the above mentioned method is quite expected.
The results obtained by using VIKOR also confirm above mentioned conclusions.However, in the case when VIKOR method is used, the second condition required in order to select the most acceptable alternative, C1, is not satisfied, and therefore the set of compromise solutions is obtained, i.e. the set which contains alternatives B 2 and B 5 .
From Table 5 can also be concluded that most of the distance-based methods stand B 2 as the most acceptable alternative.However, this is not so in the case of TOPSIS method application, one of most prominent methods.When applying TOPSIS method, the highest ranked alternative is B 4 .
Data from columns VI and VII of Table 4 and Table 5 indicate that alternatives B 4 and B 2 are real candidates for the most acceptable alternative.However, on the basis of these data the most appropriate alternative cannot be determined for certain.
It is known that the criteria weights in MCDM models have significant influence on the selection of the most acceptable alternatives.It is also known that the used normalization procedures, as well as the aggregation procedure, have significant influence on selection of the best placed alternative.
Slightly confusing results obtained when using different MCDM methods in some way indicate that this is a characteristic case where mutual influence of the relative weights of criteria, applied normalization methods and aggregation procedures is particularly emphasized.
In order to make more realistic conclusions, below are considered influence of the criteria weights and impact of normalization procedures upon ranking order of considered alternatives.

Comparative Analysis: Examining the impact of criteria weights on ranking order
In order to make more objective conclusions, in this section we reconsider the previous example of ranking banks, but with modified weights of criteria.
In the first case (Case I), all criteria have the same weight, and the resulting weights of sub-criteria are calculated using the following formula: where w j is resulting weight of j-th criterion, n sc is the number of sub-criteria of c-th criterion, and w c is weight of c-th criterion.
As shown in Table 6, criteria Liquidity, Efficiency and Profitability and Capital adequacy have the same weight, and it is 0.25.Criteria Liquidity, Efficiency and Profitability have three sub-criteria, and therefore they have the same weight, which is 0.083.Criterion Capital adequacy has four sub-criteria, which is why their weight is 0.063.
In the second case (Case II), we start from demand that the resulting weights of all subcriteria are the same, and also the following condition is satisfied: . (56) Therefore, the resulting weights of all sub-criteria have value 0.077, as shown in Table 7.
Comparative review of the best ranked alternatives, as well as ranking orders achieved in the case study, and scenarios I and II are shown in the Table 8.
From Table 8 can be concluded that changes in criteria weights may have impact on ranking order of alternatives, as shown in columns I and II, but it is not а strong rule, as shown in columns II and III.Table 6.Relative weights of evaluation criteria Table 7. Relative weights of evaluation criteria

Comparative Analysis: Examining the impact of distance metric and normalization procedure in TOPSIS method
As stated in section 2.8, when TOPSIS method is considered, ordinary TOPSIS method is based on the use of Vector normalization and Euclidean distance from the ideal and anti-ideal solution.
However, there are also some examples where TOPSIS method was used with other normalization procedures, especially in the case of fuzzy or grey extensions of TOPSIS method.In the literature the use of TOPSIS method was also considered with other metrics, such as city block distance.
In order to more accurately determine influence which normalization and aggregation procedures have, in this section are presented and discussed results of banks ranking which are obtained using some modified variants of TOPSIS method.
In column I of Table 9 are shown the results obtained by using ordinary TOPSIS method.
In column II of Table 9 are shown the results obtained by using a variant of TOPSIS method, where City block distance was used instead of Euclidean distance.In this case, replacement of distance metric has no impact on the best placed alternative, but it is reflecting on the ranking order of alternatives.
In columns III and IV, TOPSIS method was used with MaxMin normalization procedure.In column III are shown results when Euclidean distance was used, while in column IV when City block distance is used.

Table 4 .
Ranking results obtained using SAW method and various normalization procedures 1 Ranking orders of three best ranked alternatives

Table 5 .
Ranking results obtained using various MCDM methods